Monogenic function
A monogenic [1][2] function is a complex function with a single finite derivative. More precisely, a function defined on is called monogenic at , if exists and is finite, with:
Alternatively, it can be defined as the above limit having the same value for all paths. Functions can either have a single derivative (monogenic) or infinitely many derivatives (polygenic), with no intermediate cases.[2] Furthermore, a function which is monogenic , is said to be monogenic on , and if is a domain of , then it is analytic as well (The notion of domains can also be generalized [1] in a manner such that functions which are monogenic over non-connected subsets of , can show a weakened form of analyticity)
References[]
- ^ a b "Monogenic function". Encyclopedia of Math. Retrieved 15 January 2021.
- ^ a b "Monogenic Function". Wolfram MathWorld. Retrieved 15 January 2021.
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